Question: Consider a modified cost function J(X) 3 (y HX)TW(r HXJ where W is symmetric positive definite. [Q1] Show that the cost is always positive and

Consider a modified cost function J(X) 3 (y HX)TW(r HXJ where W is symmetric positive definite. [Q1] Show that the cost is always positive and zero if an only if y = Hx. [02] Show that the normal equations corresponding to solving minx J(x) are HTWHx = HTWy by taking the gradient. [Q3] We can also prove the normal equations using a linear algebra approach and orthogonality. However this requires using a very specific inner product. Can you explain how

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